A cidade de Curitiba possui 23 terminais, 6900 pontos de ônibus e 400 linhas de ônibus. Estes números expressivos não consideram a infraestrutura metropolitana, que agrega em cobertura e disponibilidade, mas também em complexidade.
Com o objetivo de viabilizar a construção da rede proposta, decidiu-se considerar apenas terminais e linhas municipais de Curitiba, bem como um subconjunto de terminais. Os terminais escolhidos foram:
Estes terminais foram escolhidos de forma arbitrária, baseando se no itinerário das linhas que por ele percorriam, bem como no conhecimento prévio dos autores em relação aos mesmos.
A partir destes terminais o script implementado (exposto na seção 3) identificou as linhas que por eles passavam, bem como os pontos de ônibus utilizados por estas linhas.
Os terminais e pontos de ônibus são identificados como nós na rede. As arestas representam por quais pontos ou terminais dada linha passa. Pontos e terminais podem estar presentem em mais de uma linha de ônibus, ou seja, são reutilizados. A capacidade de transporte de passageiros dos ônibus que percorrem uma linha é representada como o peso da aresta.
Nesse sentido, notou-se que contruir a rede reutilizando os pontos tornaria a análise de capacidade de transporte mais onerosa, visto que, ao construir a rede as capacidades iriam se sobrepor (a aresta que conecta o ponto teria que armazenar um peso para cada linha).
Por isso, decidiu-se que apenas terminais de integração seriam reutilizados. Pontos de ônibus seriam plotados de acordo com a linha e, mesmo que na vida real representassem o mesmo ponto físico, seriam plotados uma vez para cada linha que os utilizassem. Desta forma, foi possível garantir que cada aresta apresentasse apenas um peso.
Nesta seção são apresentadas as funções e os requisitos necessários para a construção da rede de capacidades.
Arquivo CSV contendo as linhas e pontos de ônibus. Este arquivo foi obtido do portal da C3SL da UFPR (https://dadosabertos.c3sl.ufpr.br/). O arquivo escolhido foi aquele gerado em 08/03/2022 (2022_03_08_pontosLinha.csv);
Terminais de Integração a serem plotados (definidos na variável "terminais").
As bibliotecas utilizadas foram:
import networkx as nx
import pandas as pd
import matplotlib.pyplot as plt
todos_pontos_linha = pd.read_csv("2022_03_08_pontosLinha.csv")
tipo_linhas_cabral = None
tipo_linhas_portao = None
tipo_linhas_pinheirinho = None
tipo_linhas_boqueirao = None
tipo_linhas_campina_do_siqueira = None
tipo_linhas_capao_da_imbuia = None
todos_tipos = None
def get_pontos_linha(codigo_linha: str, id_itineratio: int) -> pd.core.frame.DataFrame:
return todos_pontos_linha.query("COD == @codigo_linha and ITINERARY_ID == @id_itineratio").sort_values("SEQ")
def add_pontos_no_grafo(grafo: nx.classes.graph.Graph, pontos_linha: pd.core.frame.DataFrame) -> None:
for row in pontos_linha.itertuples(index=False):
NOME = getattr(row, 'NOME')
NUM = getattr(row, 'NUM')
SEQ = getattr(row, 'SEQ')
SENTIDO = getattr(row, 'SENTIDO')
ITINERARY_ID = getattr(row, 'ITINERARY_ID')
COD = getattr(row, 'COD')
#Esse linha garante que os terminais não são duplicados.
#Para isso a informação referente a linha, que consta no nome do ponto, é removida.
ID = get_id_ponto(NOME, COD, NUM)
NOME = ID if 'Terminal' in NOME else NOME
if 'Terminal' in NOME:
NOME = ID
#Codigo arbitrário para facilitar a identificação de terminais.
COD = str(999)
grafo.add_node(ID, nome=NOME, num=NUM, seq=SEQ, sentido=SENTIDO, itinerario_id=ITINERARY_ID, cod=COD)
def add_arestas_entre_pontos(grafo: nx.classes.graph.Graph, pontos_linha: pd.core.frame.DataFrame) -> None:
#Os indices das linhas do dataframe não são sequenciais, visto que, o dataframe é resultado
#de uma query.
indexes = pontos_linha.index.values.tolist()
capacidade_linha = get_capacidade_por_codigo_linha(pontos_linha.loc[indexes[0], 'COD'])
for i in range(len(pontos_linha)-1):
source = get_id_ponto(ponto_info=pontos_linha.loc[indexes[i]])
target = get_id_ponto(ponto_info=pontos_linha.loc[indexes[i+1]])
grafo.add_edge(source, target, weight=capacidade_linha)
def get_linhas_por_terminal(nome_terminal: str) -> pd.core.frame.DataFrame:
nome_terminal = f"{nome_terminal} -"
codigos_linha = todos_pontos_linha.query("NOME.str.contains(@nome_terminal)", engine="python").groupby("COD")
return list(codigos_linha.groups.keys())
# Função mantida como referência. Ver função "get_itinerario_com_terminal".
def get_itinerarios_por_linha(codigo_linha: str) -> list:
return list(todos_pontos_linha.query("COD == @codigo_linha").sort_values("ITINERARY_ID").groupby("ITINERARY_ID").groups.keys())
# Esta função garante que o itinerário retornado contém pelo menos um terminal. A função "get_itinerarios_por_linha" não tem
# essa restrição.
def get_itinerario_com_terminal(codigo_linha: str) -> list:
terminal = 'Terminal '
return list(todos_pontos_linha.query("COD == @codigo_linha and NOME.str.contains(@terminal)", engine="python").sort_values("ITINERARY_ID").groupby("ITINERARY_ID").groups.keys())
def get_id_ponto(nome_ponto: str = None, codigo_ponto: str = None, numero_ponto: int = 0, ponto_info: pd.core.series.Series = None) -> str:
if ponto_info is not None:
nome_ponto = ponto_info['NOME']
codigo_ponto = ponto_info['COD']
numero_ponto = ponto_info['NUM']
ID = None
if 'Terminal' in nome_ponto:
ID = nome_ponto.split('-')[0].strip()
else:
ID = f"{codigo_ponto}-{str(numero_ponto)}"
return ID
def get_capacidade_por_tipo_linha(tipo_linha: str) -> int:
tipo_linha = tipo_linha.upper() if tipo_linha is not None else None
# Capacidade de acordo com a categoria do veículo.
# Fonte: https://www.urbs.curitiba.pr.gov.br/transporte/rede-integrada-de-transporte/42
# Cada linha pode apresentar diferentes modelos de veículos utilizados. Comentários foram adicionados indicando o modelo escolhido.
capacidade = {
'LIGEIRÃO': 250,
'EXPRESSO': 250,#Biarticulado
'LINHA DIRETA': 110,#Padron
'INTERBAIRROS': 140,#Articulado
'ALIMENTADOR': 85,#Comum
'TRONCAL': 85,#Comum
'CONVENCIONAL': 85#Comum
}
return capacidade[tipo_linha]
def get_capacidade_por_codigo_linha(codigo_linha: str) -> str:
tipo = todos_tipos[codigo_linha]
return get_capacidade_por_tipo_linha(tipo)
# Esta função cria o mapeamento entre o código e o tipo da linha de ônibus.
def set_tipo_linhas() -> None:
# Para quase todos os dados abaixo a fonte foi https://www.urbs.curitiba.pr.gov.br/pdf/transporte/rit/Linhas_x_Empresas_Operadoras_codigo.pdf
# As exceções estão sinalizadas com comentários
global tipo_linhas_cabral, tipo_linhas_portao, tipo_linhas_pinheirinho, tipo_linhas_boqueirao, tipo_linhas_campina_do_siqueira, tipo_linhas_capao_da_imbuia
global todos_tipos
tipo_linhas_cabral = {
'020':'INTERBAIRROS',
'021':'INTERBAIRROS',
'022':'LINHA DIRETA',
'023':'LINHA DIRETA',
'200':'LIGEIRÃO',
'202':'EXPRESSO',
'203':'EXPRESSO',
'207':'TRONCAL',
'210':'LINHA DIRETA',
'211':'ALIMENTADOR',
'212':'ALIMENTADOR',
'213':'ALIMENTADOR',
'214':'ALIMENTADOR',
'216':'ALIMENTADOR',
'245':'ALIMENTADOR',
'607':'LINHA DIRETA',
'700':'LINHA DIRETA'
}
tipo_linhas_portao = {
'022':'LINHA DIRETA',
'023':'LINHA DIRETA',
'024':'LINHA DIRETA',
'050':'INTERBAIRROS',
'216':'ALIMENTADOR',
'611':'ALIMENTADOR',
'612':'ALIMENTADOR',
'615':'ALIMENTADOR',
'616':'ALIMENTADOR',
'700':'LINHA DIRETA',
'X35':'LINHA DIRETA'
}
tipo_linhas_pinheirinho = {
'040':'INTERBAIRROS',
'060':'INTERBAIRROS',
'350':'EXPRESSO',
'502':'EXPRESSO',
'507':'LINHA DIRETA',
'508':'LINHA DIRETA',
'527':'LINHA DIRETA', # Informação retirada de https://www.urbs.curitiba.pr.gov.br/pdf/transporte/rit/linhas_diretas_editada.pdf
'528':'ALIMENTADOR',
'550':'LIGEIRÃO',
'600':'ALIMENTADOR',
'602':'EXPRESSO',
'603':'EXPRESSO',
'610':'LINHA DIRETA',
'617':'ALIMENTADOR',
'630':'ALIMENTADOR',
'631':'ALIMENTADOR',
'633':'ALIMENTADOR',
'635':'ALIMENTADOR',
'636':'ALIMENTADOR',
'637':'ALIMENTADOR',
'638':'ALIMENTADOR',
'639':'ALIMENTADOR',
'640':'ALIMENTADOR',
'641':'ALIMENTADOR',
'642':'ALIMENTADOR',
'643':'ALIMENTADOR',
'644':'ALIMENTADOR',
'646':'ALIMENTADOR',
'649':'ALIMENTADOR',
'650':'ALIMENTADOR',
'655':'ALIMENTADOR',
'659':'ALIMENTADOR',
'680':'ALIMENTADOR',
'681':'ALIMENTADOR',
'690':'ALIMENTADOR',
'700':'LINHA DIRETA',
'772':'ALIMENTADOR',
'X11':'EXPRESSO',
'X20':'EXPRESSO',
'X35':'LINHA DIRETA'
}
## As linhas 539 . Optou-se por deixá-las todas como 'ALIMENTADOR'.
tipo_linhas_boqueirao = {
'335':'ALIMENTADOR',
'500':'LIGEIRÃO',
'502':'EXPRESSO',
'503':'EXPRESSO',
'505':'LINHA DIRETA',
'507':'LINHA DIRETA',
'508':'LINHA DIRETA',
'513':'ALIMENTADOR',
'515':'ALIMENTADOR',
'527':'LINHA DIRETA', # Informação retirada de https://www.urbs.curitiba.pr.gov.br/pdf/transporte/rit/linhas_diretas_editada.pdf
'528':'ALIMENTADOR',
'531':'ALIMENTADOR',
'532':'ALIMENTADOR',
'533':'ALIMENTADOR',
'534':'ALIMENTADOR',
'535':'ALIMENTADOR',
'536':'ALIMENTADOR',
'539':'ALIMENTADOR', # Informação não disponível. Trata-se de suposição.
'545':'ALIMENTADOR',
'546':'LINHA DIRETA',
'602':'EXPRESSO',
'X12':'EXPRESSO'
} # Informação retirada de https://www.urbs.curitiba.pr.gov.br/pdf/transporte/rit/expressos.pdf
## As linhas X02 e X31 não possuem caracterização do tipo de transporte. Optou-se por deixá-las todas como 'ALIMENTADOR'.
tipo_linhas_campina_do_siqueira = {
'020':'INTERBAIRROS',
'021':'INTERBAIRROS',
'022':'LINHA DIRETA',
'023':'LINHA DIRETA',
'024':'LINHA DIRETA',
'027':'INTERBAIRROS',
'303':'EXPRESSO',
'304':'LINHA DIRETA',
'801':'TRONCAL',
'811':'ALIMENTADOR',
'812':'ALIMENTADOR',
'814':'ALIMENTADOR',
'816':'ALIMENTADOR',
'X02':'ALIMENTADOR', # Informação não disponível. Trata-se de suposição.
'X31':'ALIMENTADOR'# Informação não disponível. Trata-se de suposição.
}
tipo_linhas_capao_da_imbuia = {
'020':'INTERBAIRROS',
'021':'INTERBAIRROS',
'022':'LINHA DIRETA',
'023':'LINHA DIRETA',
'302':'EXPRESSO',
'303':'EXPRESSO',
'304':'LINHA DIRETA',
'311':'ALIMENTADOR',
'X30':'LINHA DIRETA'
} # Informação retirada de https://www.urbs.curitiba.pr.gov.br/pdf/transporte/rit/linhas_diretas_editada.pdf
todos_tipos = tipo_linhas_cabral | tipo_linhas_portao | tipo_linhas_pinheirinho | tipo_linhas_boqueirao | tipo_linhas_campina_do_siqueira | tipo_linhas_capao_da_imbuia
def add_terminais_e_linhas(grafo: nx.classes.graph.Graph, terminais: list) -> None:
for terminal in terminais:
linhas = get_linhas_por_terminal(terminal)
for codigo_linha in linhas:
id_itinerario = get_itinerario_com_terminal(codigo_linha)[-1]#get_itinerarios_por_linha(codigo_linha)[-1]
pontos = get_pontos_linha(codigo_linha, id_itinerario)
add_pontos_no_grafo(grafo, pontos)
add_arestas_entre_pontos(grafo, pontos)
set_tipo_linhas()
# DiGraph representa grafos direcionados.
grafo = nx.DiGraph()
terminais = [
'Terminal Boqueirão',
'Terminal Cabral',
'Terminal Campina do Siqueira',
'Terminal Capão da Imbuia',
'Terminal Pinheirinho',
'Terminal Portão']
add_terminais_e_linhas(grafo, terminais)
# Exporta a rede gerada para o formato GML. Este arquivo foi utilizado para gerar as visualizações com o software Gephi.
nx.write_gml(grafo, 'Todos_Terminais-Directed.gml')
grafo.number_of_nodes()
1988
print(grafo.number_of_edges())
2086
# Calculando a centralidade de grau
degree_centrality = nx.degree_centrality(grafo)
# Colocando degree_centrality em ordem decrescente
degree_centrality = sorted(degree_centrality.items(), key=lambda x: x[1], reverse=True)
# Exibindo a centralidade de grau de cada nó
degree_centrality
[('Terminal Pinheirinho', 0.02415702063412179),
('Terminal Portão', 0.014091595369904378),
('Terminal Capão Raso', 0.013588324106693507),
('Terminal Boqueirão', 0.012078510317060896),
('Terminal Campina do Siqueira', 0.011575239053850024),
('Terminal Cabral', 0.011575239053850024),
('Terminal Hauer', 0.010065425264217413),
('Terminal Sítio Cercado', 0.009562154001006542),
('Terminal Capão da Imbuia', 0.008555611474584801),
('Terminal Carmo', 0.006039255158530448),
('Terminal Campo Comprido', 0.0035228988424760945),
('Terminal Boa Vista', 0.003019627579265224),
('Terminal CIC', 0.003019627579265224),
('Terminal Fazendinha', 0.0025163563160543532),
('Terminal Oficinas', 0.0025163563160543532),
('Terminal Guadalupe', 0.0020130850528434826),
('Terminal Centenário', 0.001509813789632612),
('Terminal Santa Cândida', 0.001509813789632612),
('814-190138', 0.001509813789632612),
('Terminal Tatuquara', 0.001509813789632612),
('335-140480', 0.0010065425264217413),
('335-140482', 0.0010065425264217413),
('335-140484', 0.0010065425264217413),
('335-140486', 0.0010065425264217413),
('335-140488', 0.0010065425264217413),
('335-140490', 0.0010065425264217413),
('335-140492', 0.0010065425264217413),
('335-140494', 0.0010065425264217413),
('335-140496', 0.0010065425264217413),
('335-140498', 0.0010065425264217413),
('335-140500', 0.0010065425264217413),
('335-140502', 0.0010065425264217413),
('335-140504', 0.0010065425264217413),
('335-140506', 0.0010065425264217413),
('335-140508', 0.0010065425264217413),
('335-140510', 0.0010065425264217413),
('335-140512', 0.0010065425264217413),
('335-140514', 0.0010065425264217413),
('335-140516', 0.0010065425264217413),
('335-140518', 0.0010065425264217413),
('335-140520', 0.0010065425264217413),
('500-108067', 0.0010065425264217413),
('500-108078', 0.0010065425264217413),
('502-108132', 0.0010065425264217413),
('502-108130', 0.0010065425264217413),
('502-108128', 0.0010065425264217413),
('502-108126', 0.0010065425264217413),
('502-108124', 0.0010065425264217413),
('502-108064', 0.0010065425264217413),
('502-108062', 0.0010065425264217413),
('502-108060', 0.0010065425264217413),
('502-108058', 0.0010065425264217413),
('502-108056', 0.0010065425264217413),
('502-108053', 0.0010065425264217413),
('502-108051', 0.0010065425264217413),
('502-108122', 0.0010065425264217413),
('502-108120', 0.0010065425264217413),
('502-108118', 0.0010065425264217413),
('502-108116', 0.0010065425264217413),
('502-108114', 0.0010065425264217413),
('502-108212', 0.0010065425264217413),
('502-108083', 0.0010065425264217413),
('502-108086', 0.0010065425264217413),
('502-108088', 0.0010065425264217413),
('502-108090', 0.0010065425264217413),
('502-108092', 0.0010065425264217413),
('502-108094', 0.0010065425264217413),
('502-108096', 0.0010065425264217413),
('502-108111', 0.0010065425264217413),
('502-108109', 0.0010065425264217413),
('502-108107', 0.0010065425264217413),
('502-108105', 0.0010065425264217413),
('502-108103', 0.0010065425264217413),
('502-108101', 0.0010065425264217413),
('502-108099', 0.0010065425264217413),
('502-108097', 0.0010065425264217413),
('503-108067', 0.0010065425264217413),
('503-108070', 0.0010065425264217413),
('503-108072', 0.0010065425264217413),
('503-108073', 0.0010065425264217413),
('503-108076', 0.0010065425264217413),
('503-108077', 0.0010065425264217413),
('503-108079', 0.0010065425264217413),
('503-108081', 0.0010065425264217413),
('503-108083', 0.0010065425264217413),
('503-108086', 0.0010065425264217413),
('503-108088', 0.0010065425264217413),
('503-108090', 0.0010065425264217413),
('503-108092', 0.0010065425264217413),
('503-108094', 0.0010065425264217413),
('503-108096', 0.0010065425264217413),
('505-109040', 0.0010065425264217413),
('505-109031', 0.0010065425264217413),
('505-109018', 0.0010065425264217413),
('505-109022', 0.0010065425264217413),
('505-109057', 0.0010065425264217413),
('505-109011', 0.0010065425264217413),
('507-109076', 0.0010065425264217413),
('507-109002', 0.0010065425264217413),
('507-109074', 0.0010065425264217413),
('507-110457', 0.0010065425264217413),
('507-109030', 0.0010065425264217413),
('507-109039', 0.0010065425264217413),
('507-109006', 0.0010065425264217413),
('508-109005', 0.0010065425264217413),
('508-109040', 0.0010065425264217413),
('508-109031', 0.0010065425264217413),
('508-110458', 0.0010065425264217413),
('508-109073', 0.0010065425264217413),
('508-109003', 0.0010065425264217413),
('508-109075', 0.0010065425264217413),
('513-150431', 0.0010065425264217413),
('513-150428', 0.0010065425264217413),
('513-150426', 0.0010065425264217413),
('513-150424', 0.0010065425264217413),
('513-150422', 0.0010065425264217413),
('513-150421', 0.0010065425264217413),
('513-150419', 0.0010065425264217413),
('513-150417', 0.0010065425264217413),
('513-150415', 0.0010065425264217413),
('513-150413', 0.0010065425264217413),
('513-150411', 0.0010065425264217413),
('513-150269', 0.0010065425264217413),
('513-150267', 0.0010065425264217413),
('513-150265', 0.0010065425264217413),
('513-150263', 0.0010065425264217413),
('513-150261', 0.0010065425264217413),
('513-150408', 0.0010065425264217413),
('513-150259', 0.0010065425264217413),
('513-150256', 0.0010065425264217413),
('513-150255', 0.0010065425264217413),
('513-150252', 0.0010065425264217413),
('513-150200', 0.0010065425264217413),
('513-150201', 0.0010065425264217413),
('513-150203', 0.0010065425264217413),
('513-150202', 0.0010065425264217413),
('515-140296', 0.0010065425264217413),
('515-140294', 0.0010065425264217413),
('515-140648', 0.0010065425264217413),
('515-140262', 0.0010065425264217413),
('515-140486', 0.0010065425264217413),
('515-140488', 0.0010065425264217413),
('515-140490', 0.0010065425264217413),
('515-140260', 0.0010065425264217413),
('515-140258', 0.0010065425264217413),
('515-140199', 0.0010065425264217413),
('515-140197', 0.0010065425264217413),
('515-140195', 0.0010065425264217413),
('515-140328', 0.0010065425264217413),
('515-140193', 0.0010065425264217413),
('515-140190', 0.0010065425264217413),
('515-140189', 0.0010065425264217413),
('515-140007', 0.0010065425264217413),
('515-140005', 0.0010065425264217413),
('515-140003', 0.0010065425264217413),
('515-140009', 0.0010065425264217413),
('515-140011', 0.0010065425264217413),
('515-140010', 0.0010065425264217413),
('527-109075', 0.0010065425264217413),
('527-109005', 0.0010065425264217413),
('528-150331', 0.0010065425264217413),
('528-170051', 0.0010065425264217413),
('528-170052', 0.0010065425264217413),
('528-160245', 0.0010065425264217413),
('528-160316', 0.0010065425264217413),
('528-160318', 0.0010065425264217413),
('528-160322', 0.0010065425264217413),
('528-160079', 0.0010065425264217413),
('528-160140', 0.0010065425264217413),
('528-160323', 0.0010065425264217413),
('528-160325', 0.0010065425264217413),
('528-160326', 0.0010065425264217413),
('528-160328', 0.0010065425264217413),
('528-160330', 0.0010065425264217413),
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('022-109024', 0.0010065425264217413),
('022-109034', 0.0010065425264217413),
('022-109065', 0.0010065425264217413),
('022-109077', 0.0010065425264217413),
('022-109066', 0.0010065425264217413),
('022-109046', 0.0010065425264217413),
('022-109045', 0.0010065425264217413),
('022-109011', 0.0010065425264217413),
('023-109067', 0.0010065425264217413),
('023-109077', 0.0010065425264217413),
('023-109065', 0.0010065425264217413),
('023-109034', 0.0010065425264217413),
('023-109025', 0.0010065425264217413),
('023-109021', 0.0010065425264217413),
('023-109048', 0.0010065425264217413),
('023-109001', 0.0010065425264217413),
('023-109012', 0.0010065425264217413),
('023-109069', 0.0010065425264217413),
('023-109047', 0.0010065425264217413),
('200-108031', 0.0010065425264217413),
('200-108026', 0.0010065425264217413),
('200-108023', 0.0010065425264217413),
('200-108021', 0.0010065425264217413),
('202-108056', 0.0010065425264217413),
('202-108053', 0.0010065425264217413),
('202-108051', 0.0010065425264217413),
('202-108049', 0.0010065425264217413),
('202-108047', 0.0010065425264217413),
('202-108045', 0.0010065425264217413),
('202-108043', 0.0010065425264217413),
('202-108041', 0.0010065425264217413),
('202-108039', 0.0010065425264217413),
('202-108037', 0.0010065425264217413),
('202-108035', 0.0010065425264217413),
('202-108033', 0.0010065425264217413),
('202-108031', 0.0010065425264217413),
('202-108027', 0.0010065425264217413),
('202-108026', 0.0010065425264217413),
('202-108023', 0.0010065425264217413),
('202-108021', 0.0010065425264217413),
('202-108019', 0.0010065425264217413),
('202-109147', 0.0010065425264217413),
('202-108015', 0.0010065425264217413),
('202-108013', 0.0010065425264217413),
('202-108011', 0.0010065425264217413),
('202-108009', 0.0010065425264217413),
('202-108007', 0.0010065425264217413),
('202-108008', 0.0010065425264217413),
('202-108010', 0.0010065425264217413),
('202-108012', 0.0010065425264217413),
('203-108002', 0.0010065425264217413),
('203-108004', 0.0010065425264217413),
('203-108006', 0.0010065425264217413),
('203-108008', 0.0010065425264217413),
('203-108010', 0.0010065425264217413),
('203-108012', 0.0010065425264217413),
('203-108014', 0.0010065425264217413),
('203-108016', 0.0010065425264217413),
('203-109146', 0.0010065425264217413),
('203-108020', 0.0010065425264217413),
('203-108022', 0.0010065425264217413),
('203-108024', 0.0010065425264217413),
('203-108025', 0.0010065425264217413),
('203-108028', 0.0010065425264217413),
('203-108032', 0.0010065425264217413),
('203-108034', 0.0010065425264217413),
('203-108036', 0.0010065425264217413),
('203-108038', 0.0010065425264217413),
('203-108040', 0.0010065425264217413),
('203-108042', 0.0010065425264217413),
('203-108044', 0.0010065425264217413),
('203-108046', 0.0010065425264217413),
('203-108048', 0.0010065425264217413),
('203-108050', 0.0010065425264217413),
('203-108052', 0.0010065425264217413),
('203-108054', 0.0010065425264217413),
('203-108055', 0.0010065425264217413),
('207-120001', 0.0010065425264217413),
('207-120048', 0.0010065425264217413),
('207-120049', 0.0010065425264217413),
('207-120051', 0.0010065425264217413),
('207-120053', 0.0010065425264217413),
('207-120103', 0.0010065425264217413),
('207-120101', 0.0010065425264217413),
('207-120057', 0.0010065425264217413),
('207-120058', 0.0010065425264217413),
('207-120060', 0.0010065425264217413),
('207-120066', 0.0010065425264217413),
('207-120065', 0.0010065425264217413),
('207-110131', 0.0010065425264217413),
('207-110008', 0.0010065425264217413),
('207-110133', 0.0010065425264217413),
('207-110187', 0.0010065425264217413),
('207-110122', 0.0010065425264217413),
('207-110013', 0.0010065425264217413),
('207-110014', 0.0010065425264217413),
('210-109023', 0.0010065425264217413),
('210-109056', 0.0010065425264217413),
('210-109063', 0.0010065425264217413),
('210-109035', 0.0010065425264217413),
('210-109071', 0.0010065425264217413),
('211-130087', 0.0010065425264217413),
('211-130085', 0.0010065425264217413),
('211-130285', 0.0010065425264217413),
('211-130639', 0.0010065425264217413),
('211-130082', 0.0010065425264217413),
('211-130080', 0.0010065425264217413),
('211-130077', 0.0010065425264217413),
('211-130075', 0.0010065425264217413),
('211-130068', 0.0010065425264217413),
('211-130943', 0.0010065425264217413),
('211-130650', 0.0010065425264217413),
('211-130070', 0.0010065425264217413),
('211-130071', 0.0010065425264217413),
('211-130072', 0.0010065425264217413),
('211-130073', 0.0010065425264217413),
('211-130013', 0.0010065425264217413),
('211-130003', 0.0010065425264217413),
('211-130001', 0.0010065425264217413),
('212-130036', 0.0010065425264217413),
('212-130905', 0.0010065425264217413),
('212-130032', 0.0010065425264217413),
('212-130031', 0.0010065425264217413),
('212-130030', 0.0010065425264217413),
('212-130898', 0.0010065425264217413),
('212-130028', 0.0010065425264217413),
('212-130027', 0.0010065425264217413),
('212-130025', 0.0010065425264217413),
('212-130023', 0.0010065425264217413),
('212-130021', 0.0010065425264217413),
('212-130020', 0.0010065425264217413),
('212-130018', 0.0010065425264217413),
('212-130016', 0.0010065425264217413),
('212-130014', 0.0010065425264217413),
('212-130010', 0.0010065425264217413),
('212-130011', 0.0010065425264217413),
('212-130012', 0.0010065425264217413),
('212-130013', 0.0010065425264217413),
('212-130003', 0.0010065425264217413),
('212-130001', 0.0010065425264217413),
('213-130002', 0.0010065425264217413),
('213-130004', 0.0010065425264217413),
('213-130005', 0.0010065425264217413),
('213-130006', 0.0010065425264217413),
('213-130007', 0.0010065425264217413),
('213-130008', 0.0010065425264217413),
('213-130009', 0.0010065425264217413),
('213-130015', 0.0010065425264217413),
('213-130017', 0.0010065425264217413),
('213-130019', 0.0010065425264217413),
('213-130483', 0.0010065425264217413),
('213-130041', 0.0010065425264217413),
('213-130597', 0.0010065425264217413),
('213-130600', 0.0010065425264217413),
('213-130601', 0.0010065425264217413),
('213-130602', 0.0010065425264217413),
('213-130603', 0.0010065425264217413),
('214-130919', 0.0010065425264217413),
('214-130057', 0.0010065425264217413),
('214-130056', 0.0010065425264217413),
('214-130055', 0.0010065425264217413),
('214-130052', 0.0010065425264217413),
('214-130050', 0.0010065425264217413),
('214-130047', 0.0010065425264217413),
('214-130046', 0.0010065425264217413),
('214-130044', 0.0010065425264217413),
('214-130042', 0.0010065425264217413),
('214-130040', 0.0010065425264217413),
('214-130022', 0.0010065425264217413),
('214-130020', 0.0010065425264217413),
('214-130018', 0.0010065425264217413),
('214-130016', 0.0010065425264217413),
('214-130014', 0.0010065425264217413),
('214-130010', 0.0010065425264217413),
('214-130011', 0.0010065425264217413),
('214-130012', 0.0010065425264217413),
('214-130013', 0.0010065425264217413),
('214-130003', 0.0010065425264217413),
('214-130001', 0.0010065425264217413),
('216-150023', 0.0010065425264217413),
('216-150021', 0.0010065425264217413),
('216-150019', 0.0010065425264217413),
('216-150017', 0.0010065425264217413),
('216-150015', 0.0010065425264217413),
('216-150013', 0.0010065425264217413),
('216-150011', 0.0010065425264217413),
('216-150009', 0.0010065425264217413),
('216-150248', 0.0010065425264217413),
('216-150006', 0.0010065425264217413),
('216-150004', 0.0010065425264217413),
('216-150002', 0.0010065425264217413),
('216-140053', 0.0010065425264217413),
('216-140350', 0.0010065425264217413),
('216-140351', 0.0010065425264217413),
('216-140352', 0.0010065425264217413),
('216-140048', 0.0010065425264217413),
('216-140044', 0.0010065425264217413),
('216-140043', 0.0010065425264217413),
('216-130150', 0.0010065425264217413),
('216-130916', 0.0010065425264217413),
('216-130917', 0.0010065425264217413),
('216-130136', 0.0010065425264217413),
('216-130137', 0.0010065425264217413),
('216-130138', 0.0010065425264217413),
('216-130140', 0.0010065425264217413),
('216-130142', 0.0010065425264217413),
('216-130938', 0.0010065425264217413),
('216-130105', 0.0010065425264217413),
('216-130107', 0.0010065425264217413),
('216-130108', 0.0010065425264217413),
('245-120001', 0.0010065425264217413),
('245-120003', 0.0010065425264217413),
('245-120004', 0.0010065425264217413),
('245-120005', 0.0010065425264217413),
('245-120006', 0.0010065425264217413),
('245-120011', 0.0010065425264217413),
('245-120013', 0.0010065425264217413),
('245-120016', 0.0010065425264217413),
('245-120018', 0.0010065425264217413),
('245-120019', 0.0010065425264217413),
('245-120021', 0.0010065425264217413),
('607-109071', 0.0010065425264217413),
('607-109035', 0.0010065425264217413),
('607-109068', 0.0010065425264217413),
('607-109051', 0.0010065425264217413),
('607-109022', 0.0010065425264217413),
('700-109002', 0.0010065425264217413),
('700-109074', 0.0010065425264217413),
('700-110457', 0.0010065425264217413),
('700-109030', 0.0010065425264217413),
('024-109067', 0.0010065425264217413),
('024-109066', 0.0010065425264217413),
('024-109047', 0.0010065425264217413),
('027-180127', 0.0010065425264217413),
('027-180124', 0.0010065425264217413),
('027-180123', 0.0010065425264217413),
('027-180121', 0.0010065425264217413),
('027-180117', 0.0010065425264217413),
('027-180115', 0.0010065425264217413),
('027-180111', 0.0010065425264217413),
('027-180109', 0.0010065425264217413),
('027-180105', 0.0010065425264217413),
('027-180103', 0.0010065425264217413),
('027-180101', 0.0010065425264217413),
('027-170016', 0.0010065425264217413),
('027-170013', 0.0010065425264217413),
('027-170011', 0.0010065425264217413),
('027-170009', 0.0010065425264217413),
('027-170007', 0.0010065425264217413),
('027-170006', 0.0010065425264217413),
('027-170003', 0.0010065425264217413),
('027-170001', 0.0010065425264217413),
('303-108201', 0.0010065425264217413),
('303-108199', 0.0010065425264217413),
('303-108197', 0.0010065425264217413),
('303-108195', 0.0010065425264217413),
('303-108193', 0.0010065425264217413),
('303-108191', 0.0010065425264217413),
('303-108189', 0.0010065425264217413),
('303-108187', 0.0010065425264217413),
('303-108185', 0.0010065425264217413),
('303-108183', 0.0010065425264217413),
('303-108181', 0.0010065425264217413),
('303-108179', 0.0010065425264217413),
('303-108177', 0.0010065425264217413),
('303-108176', 0.0010065425264217413),
('303-108174', 0.0010065425264217413),
('303-108169', 0.0010065425264217413),
('303-108026', 0.0010065425264217413),
('303-108168', 0.0010065425264217413),
('303-108165', 0.0010065425264217413),
('303-108163', 0.0010065425264217413),
('303-108161', 0.0010065425264217413),
('303-108159', 0.0010065425264217413),
('303-108157', 0.0010065425264217413),
('303-108155', 0.0010065425264217413),
('303-108153', 0.0010065425264217413),
('303-108151', 0.0010065425264217413),
('303-108149', 0.0010065425264217413),
('303-108147', 0.0010065425264217413),
('303-108145', 0.0010065425264217413),
('303-108143', 0.0010065425264217413),
('304-109044', 0.0010065425264217413),
('304-109052', 0.0010065425264217413),
('304-109060', 0.0010065425264217413),
('801-110020', 0.0010065425264217413),
('801-180071', 0.0010065425264217413),
('801-180070', 0.0010065425264217413),
('801-180068', 0.0010065425264217413),
('801-180066', 0.0010065425264217413),
('801-180065', 0.0010065425264217413),
('801-180060', 0.0010065425264217413),
('801-180058', 0.0010065425264217413),
('801-180056', 0.0010065425264217413),
('801-180054', 0.0010065425264217413),
('801-180052', 0.0010065425264217413),
('801-180051', 0.0010065425264217413),
('811-190135', 0.0010065425264217413),
('811-190133', 0.0010065425264217413),
('811-190131', 0.0010065425264217413),
('811-190129', 0.0010065425264217413),
('811-190127', 0.0010065425264217413),
('811-190125', 0.0010065425264217413),
('811-190123', 0.0010065425264217413),
('811-190121', 0.0010065425264217413),
('811-190120', 0.0010065425264217413),
('811-190117', 0.0010065425264217413),
('811-190115', 0.0010065425264217413),
('811-190113', 0.0010065425264217413),
('811-190111', 0.0010065425264217413),
('811-190109', 0.0010065425264217413),
('811-190107', 0.0010065425264217413),
('811-190105', 0.0010065425264217413),
('811-190103', 0.0010065425264217413),
('811-190101', 0.0010065425264217413),
('811-190016', 0.0010065425264217413),
('811-190014', 0.0010065425264217413),
('811-190198', 0.0010065425264217413),
('811-190199', 0.0010065425264217413),
('811-190011', 0.0010065425264217413),
('811-190012', 0.0010065425264217413),
('812-190068', 0.0010065425264217413),
('812-190066', 0.0010065425264217413),
('812-190064', 0.0010065425264217413),
('812-190062', 0.0010065425264217413),
('812-190060', 0.0010065425264217413),
('812-190058', 0.0010065425264217413),
('812-190056', 0.0010065425264217413),
('812-190054', 0.0010065425264217413),
('812-190052', 0.0010065425264217413),
('812-190050', 0.0010065425264217413),
('812-190942', 0.0010065425264217413),
('812-190046', 0.0010065425264217413),
('812-190044', 0.0010065425264217413),
('812-190042', 0.0010065425264217413),
('812-190040', 0.0010065425264217413),
('812-190038', 0.0010065425264217413),
('812-190036', 0.0010065425264217413),
('812-190034', 0.0010065425264217413),
('812-190032', 0.0010065425264217413),
('812-190022', 0.0010065425264217413),
('812-190020', 0.0010065425264217413),
('812-190018', 0.0010065425264217413),
('812-190016', 0.0010065425264217413),
('812-190014', 0.0010065425264217413),
('812-190198', 0.0010065425264217413),
('812-190199', 0.0010065425264217413),
('812-190011', 0.0010065425264217413),
('812-190012', 0.0010065425264217413),
('814-190139', 0.0010065425264217413),
('814-190007', 0.0010065425264217413),
('814-190008', 0.0010065425264217413),
('814-190009', 0.0010065425264217413),
('814-190198', 0.0010065425264217413),
('814-190199', 0.0010065425264217413),
('814-190011', 0.0010065425264217413),
('814-190012', 0.0010065425264217413),
('814-190001', 0.0010065425264217413),
('814-190004', 0.0010065425264217413),
('814-190002', 0.0010065425264217413),
('814-190003', 0.0010065425264217413),
('814-190005', 0.0010065425264217413),
('814-190140', 0.0010065425264217413),
('814-190142', 0.0010065425264217413),
('814-190144', 0.0010065425264217413),
('814-190146', 0.0010065425264217413),
('814-180018', 0.0010065425264217413),
('814-180011', 0.0010065425264217413),
('814-180013', 0.0010065425264217413),
('814-180015', 0.0010065425264217413),
('Terminal Santa Felicidade', 0.0010065425264217413),
('816-190326', 0.0010065425264217413),
('816-190779', 0.0010065425264217413),
('816-190780', 0.0010065425264217413),
('816-190330', 0.0010065425264217413),
('816-190957', 0.0010065425264217413),
('816-190955', 0.0010065425264217413),
('816-190953', 0.0010065425264217413),
('816-190951', 0.0010065425264217413),
('816-190028', 0.0010065425264217413),
('816-190949', 0.0010065425264217413),
('816-190948', 0.0010065425264217413),
('816-190198', 0.0010065425264217413),
('816-190199', 0.0010065425264217413),
('816-190011', 0.0010065425264217413),
('816-190012', 0.0010065425264217413),
('X31-108184', 0.0010065425264217413),
('X31-108186', 0.0010065425264217413),
('X31-108188', 0.0010065425264217413),
('302-140732', 0.0010065425264217413),
('302-108146', 0.0010065425264217413),
('302-108148', 0.0010065425264217413),
('302-108150', 0.0010065425264217413),
('302-108152', 0.0010065425264217413),
('302-108154', 0.0010065425264217413),
('302-108156', 0.0010065425264217413),
('302-108158', 0.0010065425264217413),
('302-108160', 0.0010065425264217413),
('302-108162', 0.0010065425264217413),
('302-108164', 0.0010065425264217413),
('302-108166', 0.0010065425264217413),
('302-108167', 0.0010065425264217413),
('302-108025', 0.0010065425264217413),
('311-130262', 0.0010065425264217413),
('311-130204', 0.0010065425264217413),
('311-130257', 0.0010065425264217413),
('311-130255', 0.0010065425264217413),
('311-130187', 0.0010065425264217413),
...]
# Calculando a centralidade de intermediação
betweenness_centrality = nx.betweenness_centrality(grafo)
# Colocando betweenness centrality em ordem decrescente
betweenness_centrality = sorted(betweenness_centrality.items(), key=lambda x: x[1], reverse=True)
# Exibindo a centralidade de intermediação de cada nó
betweenness_centrality
[('Terminal Pinheirinho', 0.35290831323373856),
('Terminal Portão', 0.24818275825426928),
('Terminal Capão Raso', 0.1858644380821721),
('Terminal Campina do Siqueira', 0.17341513054052793),
('Terminal Hauer', 0.14406395008305847),
('Terminal Cabral', 0.12248142635083732),
('Terminal Sítio Cercado', 0.11182845427132507),
('Terminal Boqueirão', 0.10958313630744855),
('Terminal Capão da Imbuia', 0.08868420159029664),
('022-109077', 0.06849688297870356),
('Terminal Carmo', 0.05618280319221574),
('Terminal Fazendinha', 0.05368758967528613),
('023-109067', 0.042761459050798936),
('024-109067', 0.042761459050798936),
('507-109006', 0.04074465732531676),
('023-109077', 0.03952387396222495),
('Terminal Campo Comprido', 0.03841485263477457),
('507-109076', 0.03762417276581087),
('022-109034', 0.037287687187261),
('022-109065', 0.037232443916676926),
('023-109012', 0.036080951157346455),
('023-109069', 0.03602570788676238),
('023-109047', 0.03597046461617831),
('617-150331', 0.03473357285599093),
('617-160301', 0.034678329585406856),
('617-160078', 0.034623086314822776),
('617-160438', 0.034567843044238704),
('617-170121', 0.03451259977365463),
('617-160074', 0.03445735650307056),
('617-170378', 0.034402113232486486),
('617-170379', 0.034346869961902414),
('617-170908', 0.03429162669131834),
('617-170500', 0.03423638342073427),
('617-170732', 0.03418114015015019),
('617-170503', 0.03412589687956612),
('617-170505', 0.034070653608982045),
('617-170507', 0.03401541033839797),
('617-170509', 0.0339601670678139),
('617-170511', 0.03390492379722983),
('617-170513', 0.033849680526645755),
('617-170710', 0.033794437256061675),
('617-170515', 0.0337391939854776),
('617-170980', 0.03368395071489353),
('617-170733', 0.03362870744430946),
('617-170734', 0.033573464173725386),
('Terminal Tatuquara', 0.03351822090314131),
('023-109065', 0.03149043809940838),
('023-109034', 0.03143519482882428),
('022-109066', 0.031195047094466025),
('024-109066', 0.031195047094466025),
('050-170030', 0.030097615028061714),
('050-170015', 0.030042371757477638),
('050-170024', 0.029987128486893562),
('050-170022', 0.02993188521630949),
('050-170020', 0.029876641945725414),
('050-170018', 0.02982139867514134),
('Terminal Oficinas', 0.029787779681727803),
('050-180043', 0.02976615540455726),
('050-180045', 0.02971091213397319),
('050-180047', 0.029655668863389117),
('050-180049', 0.02960042559280504),
('050-180007', 0.02954518232222097),
('050-180004', 0.029489939051636896),
('050-180002', 0.029434695781052823),
('611-180001', 0.029071897849617678),
('611-180003', 0.029016654579033605),
('611-180005', 0.028961411308449533),
('611-180008', 0.028906168037865457),
('611-180010', 0.028850924767281384),
('611-180021', 0.028795681496697312),
('611-180023', 0.02874043822611324),
('611-180025', 0.028685194955529163),
('611-180027', 0.02862995168494509),
('611-180029', 0.02857470841436102),
('611-180031', 0.028519465143776943),
('611-180033', 0.02846422187319287),
('611-180103', 0.028408978602608798),
('022-109046', 0.028365307699104017),
('611-180571', 0.028353735332024725),
('022-109045', 0.028310064428519938),
('022-109011', 0.02825482115793586),
('Terminal CIC', 0.027721816513615747),
('040-180100', 0.024143843340221002),
('040-180129', 0.024088600069636926),
('040-180131', 0.024033356799052854),
('040-180133', 0.02397811352846878),
('040-180135', 0.02392287025788471),
('040-180137', 0.023867626987300633),
('040-180139', 0.02381238371671656),
('040-181021', 0.023757140446132488),
('040-180172', 0.023701897175548412),
('040-180174', 0.02364665390496434),
('040-180176', 0.023591410634380267),
('040-180178', 0.023536167363796195),
('040-180214', 0.02348092409321212),
('040-180216', 0.023425680822628046),
('040-180219', 0.023370437552043974),
('040-180222', 0.0233151942814599),
('040-180223', 0.023259951010875825),
('040-180225', 0.023204707740291753),
('040-180227', 0.02314946446970768),
('210-109023', 0.022170036759581804),
('210-109056', 0.02211479348899774),
('210-109063', 0.02205955021841367),
('210-109035', 0.0220043069478296),
('210-109071', 0.021949063677245532),
('528-150331', 0.020910844963562245),
('528-170051', 0.020855601692978173),
('528-170052', 0.0208003584223941),
('528-160245', 0.020745115151810024),
('528-160316', 0.020689871881225952),
('528-160318', 0.02063462861064188),
('528-160322', 0.020579385340057807),
('528-160079', 0.02052414206947373),
('528-160140', 0.02046889879888966),
('528-160323', 0.020413655528305586),
('528-160325', 0.020358412257721514),
('528-160326', 0.020303168987137438),
('528-160328', 0.020247925716553365),
('528-160330', 0.020192682445969293),
('528-160333', 0.020137439175385217),
('528-160335', 0.020082195904801144),
('528-160336', 0.020026952634217072),
('528-160338', 0.019971709363633),
('528-160340', 0.019916466093048923),
('528-160343', 0.01986122282246485),
('303-108151', 0.019859955774974392),
('528-160062', 0.01980597955188078),
('303-108149', 0.019804712504390316),
('528-160065', 0.019750736281296706),
('528-160066', 0.01969549301071263),
('528-160787', 0.019640249740128558),
('528-160788', 0.019585006469544485),
('528-160789', 0.01952976319896041),
('508-109075', 0.019507344905362455),
('527-109075', 0.019507344905362455),
('610-109075', 0.019507344905362455),
('528-160790', 0.019474519928376337),
('528-160791', 0.019419276657792264),
('528-160793', 0.019364033387208192),
('528-160795', 0.019308790116624116),
('528-160797', 0.019253546846040043),
('528-160750', 0.01919830357545597),
('528-160748', 0.0191430603048719),
('528-160468', 0.019087817034287823),
('528-160744', 0.01903257376370375),
('681-170478', 0.01903257376370375),
('528-160742', 0.018977330493119678),
('681-170954', 0.018977330493119678),
('528-160157', 0.0189220872225356),
('681-170956', 0.0189220872225356),
('528-160155', 0.01886684395195153),
('681-170973', 0.01886684395195153),
('528-160015', 0.018811600681367457),
('681-170975', 0.018811600681367457),
('528-160014', 0.018756357410783384),
('681-170998', 0.018756357410783384),
('528-160012', 0.01870111414019931),
('681-171051', 0.01870111414019931),
('528-160740', 0.018645870869615236),
('681-170999', 0.018645870869615236),
('528-160203', 0.018590627599031163),
('681-170919', 0.018590627599031163),
('528-160154', 0.01853538432844709),
('681-170917', 0.01853538432844709),
('528-160201', 0.018480141057863015),
('681-170915', 0.018480141057863015),
('528-150042', 0.018424897787278943),
('681-170913', 0.018424897787278943),
('528-150143', 0.01836965451669487),
('681-170911', 0.01836965451669487),
('528-150142', 0.018314411246110794),
('681-170506', 0.018314411246110794),
('528-150140', 0.01825916797552672),
('681-170504', 0.01825916797552672),
('528-150138', 0.01820392470494265),
('681-171046', 0.01820392470494265),
('528-150136', 0.018148681434358577),
('681-170490', 0.018148681434358577),
('528-150134', 0.0180934381637745),
('681-160072', 0.0180934381637745),
('681-160073', 0.01803819489319043),
('681-160075', 0.017982951622606356),
('681-160076', 0.017927708352022283),
('681-160077', 0.017872465081438207),
('681-150334', 0.017817221810854135),
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('681-150332', 0.01754100545793377),
('772-150331', 0.017508062223181797),
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('545-160027', 0.017158103706316635),
('545-160052', 0.017102860435732562),
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('545-160050', 0.01704761716514849),
('545-160249', 0.016992373894564414),
('545-160250', 0.01693713062398034),
('545-160044', 0.01688188735339627),
('060-170983', 0.01686262823154127),
('545-160042', 0.016826644082812196),
('060-170123', 0.016807384960957197),
('545-160040', 0.01677140081222812),
('060-170052', 0.016752141690373125),
('545-160141', 0.016716157541644048),
('060-160078', 0.01669689841978905),
('772-160078', 0.016694617734306222),
('545-160080', 0.016660914271059975),
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('545-170121', 0.016605671000475903),
('060-170121', 0.016586411878620904),
('545-160074', 0.016550427729891827),
('060-170682', 0.01653116860803683),
('545-170491', 0.016495184459307755),
('060-170115', 0.016475925337452756),
('545-170492', 0.016439941188723682),
('060-170683', 0.016420682066868683),
('545-170145', 0.016384697918139606),
('060-170117', 0.01636543879628461),
('545-170141', 0.016329454647555534),
('060-170118', 0.016310195525700535),
('772-160438', 0.016287135261374156),
('545-170138', 0.01627421137697146),
('060-170119', 0.016254952255116462),
('545-170136', 0.01621896810638739),
('060-170065', 0.01619970898453239),
('607-109071', 0.016176226371042254),
('545-170135', 0.016163724835803313),
('060-170063', 0.016144465713948317),
('607-109035', 0.016120983100458182),
('545-170130', 0.01610848156521924),
('060-170061', 0.01608922244336424),
('607-109068', 0.01606573982987411),
('545-170131', 0.016053238294635168),
('060-170059', 0.01603397917278017),
('607-109051', 0.016010496559290033),
('545-170132', 0.015997995024051095),
('060-170057', 0.015978735902196096),
('607-109022', 0.01595525328870596),
('545-170133', 0.01594275175346702),
('060-170050', 0.015923492631612024),
('545-170127', 0.015887508482882947),
('772-170121', 0.01587914596944591),
('060-170029', 0.015868249361027948),
('545-170126', 0.015832265212298875),
('060-170027', 0.015813006090443876),
('545-180170', 0.0157770219417148),
('060-180213', 0.015757762819859803),
('Terminal Boa Vista', 0.015727353680088752),
('545-180169', 0.015721778671130726),
('060-180211', 0.015702519549275727),
('545-180167', 0.015666535400546654),
('060-180209', 0.015647276278691655),
('545-180166', 0.01561129212996258),
('060-180207', 0.015592033008107582),
('545-180164', 0.015556048859378507),
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('545-180162', 0.015500805588794433),
('060-180205', 0.015481546466939436),
('772-160074', 0.015470649858521476),
('545-180159', 0.01544556231821036),
('060-180203', 0.015426303196355361),
('642-150331', 0.01542376910137444),
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('060-180201', 0.015371059925771289),
('545-180156', 0.015335075777042214),
('060-180199', 0.015315816655187215),
('545-180153', 0.01527983250645814),
('Terminal Caiuá', 0.015260573384603142),
('050-140246', 0.015236246072786301),
('545-180152', 0.015224589235874065),
('060-180197', 0.015205330114019068),
('659-150332', 0.015187844858650714),
('050-140293', 0.015181002802202229),
('545-180150', 0.015169345965289993),
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('050-140234', 0.015125759531618155),
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('050-140255', 0.015070516261034082),
('772-170378', 0.015061646928600859),
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('642-170051', 0.015016033218944284),
('050-140290', 0.015015272990450008),
('545-180143', 0.015003616153537772),
('060-180189', 0.014984357031682775),
('050-140168', 0.014960029719865934),
('545-180142', 0.0149483728829537),
('060-180187', 0.0149291137610987),
('050-140289', 0.014904786449281861),
('060-180185', 0.014873870490514628),
('050-140288', 0.014849543178697787),
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('050-140286', 0.014794299908113715),
('060-180181', 0.014763383949346481),
('050-140282', 0.01473905663752964),
('060-190238', 0.014708140678762407),
('050-140278', 0.014683813366945568),
('060-190362', 0.014652897408178335),
('772-170379', 0.014652137179684058),
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('646-150331', 0.014590051852651498),
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('638-150751', 0.007604565628245225),
('636-150330', 0.007599244028785291),
('616-150024', 0.007593922429325359),
('531-150025', 0.007593922429325357),
('212-130001', 0.007593922429325357),
('020-170012', 0.007591134924846345),
('021-180117', 0.007591134924846345),
('642-160731', 0.007590121286853976),
('515-140011', 0.007585306506390227),
('214-130003', 0.007585306506390227),
('646-170544', 0.007580998544922661),
('655-170710', 0.007580998544922661),
('641-160330', 0.007562753061060031),
('335-140506', 0.007560725785075295),
('631-150839', 0.007560725785075295),
('690-171031', 0.007553630319128717),
('020-170014', 0.007535891654262271),
('021-180115', 0.007535891654262271),
('515-140010', 0.007530063235806153),
('214-130001', 0.007530063235806153),
('207-120048', 0.007508016609472142),
('335-140508', 0.007505482514491221),
('631-150840', 0.007505482514491221),
('020-170015', 0.007480648383678197),
('021-180111', 0.007480648383678197),
('027-180127', 0.007455560843367082),
('335-140510', 0.007450239243907148),
('631-150841', 0.007450239243907148),
('020-180102', 0.007425405113094124),
('021-180109', 0.007425405113094124),
('027-180124', 0.0074003175727830085),
('335-140512', 0.007394995973323075),
('631-150842', 0.007394995973323075),
('020-181048', 0.0073701618425100505),
('021-180105', 0.0073701618425100505),
('027-180123', 0.007345074302198935),
('659-170558', 0.007343807254708475),
('335-140514', 0.007339752702739001),
('631-150843', 0.007339752702739001),
('020-180106', 0.007314918571925977),
('021-180103', 0.007314918571925977),
('027-180121', 0.007289831031614861),
('643-160327', 0.007288057165128217),
('335-140516', 0.007284509432154928),
('631-150844', 0.007284509432154928),
('812-190022', 0.007272852595242693),
('630-160072', 0.007272852595242692),
('020-180107', 0.007259675301341904),
('021-180101', 0.007259675301341904),
('680-160077', 0.007257648025357167),
('811-190014', 0.007252579835395327),
('536-150142', 0.007252579835395325),
('639-160317', 0.007252579835395325),
('535-150140', 0.007247511645433484),
('638-160244', 0.007247511645433484),
('636-150751', 0.0072424434554716425),
('616-150863', 0.0072373752655098015),
('531-150027', 0.007237375265509801),
('212-130003', 0.007237375265509801),
('027-180117', 0.007234587761030788),
('640-150332', 0.00723230707554796),
('335-140518', 0.007229266161570855),
('631-150271', 0.007229266161570855),
('020-180110', 0.0072044320307578305),
('021-170016', 0.0072044320307578305),
('772-170580', 0.007194295650834148),
('027-180115', 0.007179344490446714),
('335-140520', 0.007174022890986781),
('631-150272', 0.007174022890986781),
('642-160729', 0.007172755843496321),
('646-170546', 0.00716413992056119),
('655-170515', 0.00716413992056119),
('020-180112', 0.007149188760173757),
('021-170013', 0.007149188760173757),
('641-160333', 0.007146908074690928),
('690-171032', 0.007138292151755797),
('027-180111', 0.007124101219862641),
('207-120049', 0.007095212537080144),
('020-180114', 0.007093945489589684),
('021-170011', 0.007093945489589684),
('213-130002', 0.007086596614145013),
('027-180109', 0.007068857949278568),
('202-108049', 0.007043516999469359),
('203-108014', 0.007043516999469359),
('303-108187', 0.007043516999469359),
('637-160023', 0.007043516999469359),
('020-180118', 0.0070387022190056105),
('021-170009', 0.0070387022190056105),
('027-180105', 0.007013614678694494),
('202-108047', 0.006988273728885286),
('203-108016', 0.006988273728885286),
('303-108185', 0.006988273728885286),
('637-160025', 0.006988273728885286),
('020-181052', 0.006983458948421537),
('021-170007', 0.006983458948421537),
('659-170560', 0.0069814316724368004),
('027-180103', 0.006958371408110421),
('202-108045', 0.006933030458301213),
('203-109146', 0.006933030458301213),
('303-108183', 0.006933030458301213),
('637-160027', 0.006933030458301213),
('643-160329', 0.006928469087335556),
('020-180122', 0.006928215677837464),
('021-170006', 0.006928215677837464),
('812-190032', 0.006914024745944308),
('630-160071', 0.006914024745944307),
('027-180101', 0.006903128137526348),
('680-160076', 0.006899580404553058),
('811-190016', 0.0068947656240893095),
('536-150143', 0.006894765624089309),
('639-160319', 0.006894765624089309),
('535-150142', 0.00688995084362556),
('638-160317', 0.00688995084362556),
('636-160244', 0.00688513606316181),
('616-150768', 0.006880321282698061),
('531-150029', 0.00688032128269806),
('212-130013', 0.00688032128269806),
('202-108043', 0.006877787187717139),
('203-108020', 0.006877787187717139),
('303-108181', 0.006877787187717139),
('637-160231', 0.006877787187717139),
('640-150330', 0.0068755065022343105),
('020-180125', 0.006872972407253391),
('021-170003', 0.00687297240725339),
('635-150332', 0.006870691721770562),
('027-170016', 0.006847884866942274),
('202-108041', 0.006822543917133066),
('203-108022', 0.006822543917133066),
('303-108179', 0.006822543917133066),
('637-160233', 0.006822543917133066),
('020-180126', 0.006817729136669317),
('021-170001', 0.006817729136669316),
('027-170013', 0.006792641596358201),
('772-170582', 0.0067751563409898475),
('202-108039', 0.006767300646548993),
('203-108024', 0.006767300646548993),
('303-108177', 0.006767300646548993),
('637-160235', 0.006767300646548993),
...]
# Calculando a centralidade de proximidade
closeness_centrality = nx.closeness_centrality(grafo)
# Colocando closeness centrality em ordem decrescente
closeness_centrality = sorted(closeness_centrality.items(), key=lambda x: x[1], reverse=True)
# Exibindo a centralidade de proximidade de cada nó
closeness_centrality
[('Terminal Capão Raso', 0.053349912176243165),
('Terminal Pinheirinho', 0.05329973984504293),
('Terminal Portão', 0.05323507341573698),
('Terminal Hauer', 0.05017741481649312),
('528-150331', 0.05017741481649312),
('617-150331', 0.050168161429775225),
('020-170002', 0.05016076117732403),
('060-170983', 0.050158911455324716),
('021-150169', 0.05015336310775767),
('Terminal CIC', 0.05014596722011044),
('607-109071', 0.05013857351341722),
('350-108203', 0.050133061661336145),
('550-108203', 0.050133061661336145),
('600-150331', 0.050133061661336145),
('641-150331', 0.050133061661336145),
('642-150331', 0.050133061661336145),
('646-150331', 0.050133061661336145),
('655-150331', 0.050133061661336145),
('690-150331', 0.050133061661336145),
('772-150331', 0.050133061661336145),
('507-109002', 0.0501330296640681),
('602-108057', 0.050127487040556314),
('502-108056', 0.05012563977172375),
('202-108056', 0.05012563977172375),
('603-108056', 0.05012563977172375),
('X20-108056', 0.05012563977172375),
('023-109077', 0.05012379263903511),
('631-150331', 0.05011271270108299),
('040-170053', 0.05009056751410406),
('602-108123', 0.05008687855232521),
('216-150023', 0.05008503427518579),
('502-108064', 0.0500831901338597),
('603-108064', 0.0500831901338597),
('X20-108064', 0.0500831901338597),
('631-150845', 0.05008134612833195),
('508-109075', 0.05007950225858752),
('527-109075', 0.05007950225858752),
('610-109075', 0.05007950225858752),
('700-109002', 0.05007591631233256),
('603-108049', 0.05007591631233256),
('050-170030', 0.050068441890731244),
('202-108049', 0.05006107102592822),
('Terminal Campina do Siqueira', 0.0500500187969789),
('502-108122', 0.05003713069619981),
('602-108052', 0.050024249231197665),
('203-108052', 0.050024249231197665),
('022-109066', 0.0500224095633089),
('024-109066', 0.0500224095633089),
('Terminal Sítio Cercado', 0.049140511591239),
('Terminal Carmo', 0.04809282469488724),
('528-170051', 0.047400660748727896),
('617-160301', 0.04738414829114108),
('060-170123', 0.04736764733408189),
('505-109040', 0.04736426181720851),
('020-150204', 0.047334679873520864),
('021-140013', 0.04733303270506649),
('020-170004', 0.04733138565124559),
('040-180074', 0.047329738712046196),
('602-108085', 0.0473264451774641),
('350-108205', 0.047326399144681654),
('550-108205', 0.047326399144681654),
('600-160301', 0.047326399144681654),
('641-170051', 0.047326399144681654),
('642-170051', 0.047326399144681654),
('646-160301', 0.047326399144681654),
('655-160301', 0.047326399144681654),
('690-160301', 0.047326399144681654),
('772-160301', 0.047326399144681654),
('612-170613', 0.04732150573495323),
('021-150070', 0.047318213346047994),
('023-109065', 0.04731656732339012),
('502-108088', 0.047314921415246125),
('503-108088', 0.047314921415246125),
('022-109077', 0.047313275621604076),
('644-170086', 0.0473083389275701),
('607-109035', 0.04729189071849995),
('216-150021', 0.04728695848585071),
('631-170051', 0.04728531463691495),
('507-109074', 0.04728202728189292),
('700-109074', 0.047275531716157795),
('603-108047', 0.047275531716157795),
('602-108059', 0.0472721679587647),
('502-108053', 0.04726888243138364),
('202-108053', 0.04726888243138364),
('603-108053', 0.04726888243138364),
('X20-108053', 0.04726888243138364),
('020-190201', 0.04725738668121793),
('050-170015', 0.04725738668121793),
('040-170054', 0.04724589652120512),
('202-108047', 0.04724425552587599),
('602-108125', 0.04723933322377911),
('303-108187', 0.047237692684337404),
('502-108062', 0.04723277174961788),
('021-180127', 0.04723277174961788),
('603-108062', 0.04723277174961788),
('X20-108062', 0.04723277174961788),
('027-180127', 0.047231131665873664),
('631-150846', 0.04722949169602415),
('814-190001', 0.04721801509513297),
('304-109044', 0.04721309825912862),
('022-109046', 0.047206544070434356),
('502-108120', 0.047201629622982806),
('023-109067', 0.0471999917012109),
('024-109067', 0.0471999917012109),
('024-109047', 0.04719671619866397),
('602-108054', 0.047178709057802214),
('203-108054', 0.047178709057802214),
('Terminal Boqueirão', 0.04685207222532019),
('545-160023', 0.04648222536464121),
('649-150610', 0.04642669673170508),
('637-160023', 0.04641719085604339),
('534-150363', 0.046412439377810616),
('602-108098', 0.046401356377345146),
('502-108132', 0.046396608140174496),
('Terminal Capão da Imbuia', 0.046396608140174496),
('X20-108132', 0.046396608140174496),
('507-109076', 0.04639027866871852),
('508-109005', 0.04639027866871852),
('527-109005', 0.04639027866871852),
('546-109005', 0.04639027866871852),
('508-109040', 0.04545698495623753),
('602-108091', 0.04545698495623753),
('502-108094', 0.045455465875066686),
('503-108094', 0.045455465875066686),
('528-170052', 0.04491511560049847),
('617-160078', 0.04489287966089626),
('060-170052', 0.04487066572690822),
('505-109031', 0.04485413618071066),
('350-108207', 0.04482166123931895),
('550-108207', 0.04482166123931895),
('600-160078', 0.04482166123931895),
('641-170052', 0.04482166123931895),
('642-170052', 0.04482166123931895),
('646-160078', 0.04482166123931895),
('655-160078', 0.04482166123931895),
('690-160078', 0.04482166123931895),
('772-160078', 0.04482166123931895),
('040-180076', 0.04481301225069995),
('020-170005', 0.044804155632448224),
('612-170611', 0.044798253164888044),
('020-150205', 0.0447967777909859),
('021-140035', 0.04479382733469985),
('021-150071', 0.04478645289405998),
('216-150019', 0.04478497829729671),
('602-108084', 0.04478202939505813),
('700-110457', 0.04477608836062766),
('603-108045', 0.04477608836062766),
('644-170084', 0.044774658838194),
('023-109034', 0.04476434413366339),
('502-108090', 0.04476139794805501),
('503-108090', 0.04476139794805501),
('020-190202', 0.044759925000674446),
('631-170052', 0.044759925000674446),
('607-109068', 0.04475108935171889),
('050-170024', 0.04474520085678791),
('507-110457', 0.044737842416968016),
('202-108045', 0.04472754466625549),
('602-108061', 0.044724603322444205),
('303-108185', 0.044724603322444205),
('502-108051', 0.044720192032006036),
('202-108051', 0.044720192032006036),
('603-108051', 0.044720192032006036),
('X20-108051', 0.044720192032006036),
('021-180124', 0.044715781611673486),
('027-180124', 0.044712841814716665),
('040-170055', 0.044706963380295665),
('602-108127', 0.044698148626252696),
('502-108060', 0.04468933734748811),
('814-190004', 0.04468933734748811),
('603-108060', 0.04468933734748811),
('X20-108060', 0.04468933734748811),
('631-150847', 0.044684933010693026),
('304-109052', 0.0446805295419471),
('502-108118', 0.04467025815584551),
('022-109045', 0.04466879120046947),
('602-108055', 0.04463947231287111),
('203-108055', 0.04463947231287111),
('335-140480', 0.044388909729644474),
('513-150431', 0.04438021993688197),
('515-140296', 0.0443758763162435),
('545-150026', 0.04435995697894843),
('502-108111', 0.044355617323599286),
('X12-108111', 0.044355617323599286),
('507-109006', 0.04434549476234785),
('602-108095', 0.04434549476234785),
('545-160025', 0.04409678275450611),
('649-150609', 0.043996938829263026),
('Terminal Pinhais', 0.04398503391351322),
('302-108154', 0.04398503391351322),
('637-160025', 0.043979868108041116),
('021-130230', 0.04397275921654853),
('534-150364', 0.04397133771402003),
('020-140125', 0.04395286654103776),
('602-108100', 0.04395144632433423),
('023-109025', 0.04394576637520986),
('502-108130', 0.04394292695113703),
('X20-108130', 0.04394292695113703),
('022-109034', 0.04394008789396226),
('303-108151', 0.04394008789396226),
('X30-420102', 0.04393866850293942),
('Terminal Cabral', 0.043894712819333145),
('508-109031', 0.04309505943178708),
('602-108089', 0.04309505943178708),
('502-108096', 0.04309232887202584),
('503-108096', 0.04309232887202584),
('528-160245', 0.042677251532551946),
('617-160438', 0.04265048792316241),
('060-160078', 0.04262375786053822),
('505-109018', 0.042600579105884565),
('350-108209', 0.042572616857891245),
('550-108209', 0.042572616857891245),
('600-160438', 0.042572616857891245),
('641-160245', 0.042572616857891245),
('642-160245', 0.042572616857891245),
('646-160438', 0.042572616857891245),
('655-160438', 0.042572616857891245),
('690-160438', 0.042572616857891245),
('772-160438', 0.042572616857891245),
('040-180078', 0.042550422649779325),
('216-150017', 0.04253445576301622),
('020-170008', 0.042533125730002994),
('700-109030', 0.04253155045086525),
('603-108043', 0.04253155045086525),
('612-170988', 0.042530465913498086),
('Terminal Guadalupe', 0.04252381782741413),
('020-150206', 0.04251717181937659),
('020-190203', 0.04251318521161105),
('021-140179', 0.04251318521161105),
('021-150072', 0.042511856508485296),
('644-170072', 0.042498574043788526),
('602-108211', 0.04249724625380372),
('631-170122', 0.04249060854821616),
('050-170022', 0.042486626920052964),
('502-108092', 0.04246938181733158),
('503-108092', 0.04246938181733158),
('607-109051', 0.04246938181733158),
('202-108043', 0.0424654041661358),
('303-108183', 0.0424654041661358),
('507-109030', 0.04245347568181946),
('021-180123', 0.04245347568181946),
('027-180123', 0.0424495010094403),
('602-108063', 0.04243758145655484),
('040-170070', 0.04242699191657815),
('814-190002', 0.04241773040338964),
('602-108129', 0.04241640766014393),
('502-108058', 0.0424058286832989),
('304-109060', 0.0424058286832989),
('603-108058', 0.0424058286832989),
('X20-108058', 0.0424058286832989),
('631-150279', 0.04240054117348802),
('502-108116', 0.04239657640636772),
('022-109011', 0.042389970108623026),
('335-140482', 0.042171803833493386),
('513-150428', 0.0421561197807443),
('515-140294', 0.042148282128330924),
('545-150028', 0.04211956898635956),
('502-108109', 0.042111744917817204),
('X12-108109', 0.042111744917817204),
('602-108093', 0.042093500057111335),
('545-160027', 0.04194422772350352),
('302-108156', 0.041815532561255614),
('649-150608', 0.041808857221537335),
('021-130228', 0.0417895898751266),
('637-160027', 0.04178573853666428),
('534-150348', 0.04177418877938317),
('020-140167', 0.041753671634757517),
('602-108102', 0.04174726415952046),
('023-109021', 0.0417408586505507),
('502-108128', 0.0417357356584792),
('X20-108128', 0.0417357356584792),
('Terminal Boa Vista', 0.041733174633985695),
('207-120001', 0.04173274354273883),
('213-130002', 0.04173274354273883),
('245-120001', 0.04173274354273883),
('022-109065', 0.04173061392377652),
('303-108149', 0.04173061392377652),
('X30-108137', 0.04172805352779383),
('020-130110', 0.041719094615553176),
('203-108014', 0.04171397696410377),
('210-109023', 0.04169735326463001),
('022-109001', 0.04169479694833386),
('023-109012', 0.0416922409454558),
('202-108011', 0.0416922409454558),
('602-108087', 0.04096645968272432),
('528-160316', 0.04065180397027782),
('617-170121', 0.040621453213244604),
('060-160438', 0.04059114774233052),
('505-109022', 0.04056616717633574),
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('213-130017', 0.03000595537844491),
('245-120018', 0.03000595537844491),
('545-150132', 0.02999888317333809),
('302-108148', 0.029988962251592824),
('021-130029', 0.029909830482342626),
('649-150596', 0.0299091728054333),
('020-130126', 0.029873701151838173),
('637-160031', 0.02986582998519005),
('203-108032', 0.029850100088779315),
('214-130047', 0.0298468251123581),
('534-150123', 0.029844205648583616),
('020-140011', 0.029818036276947093),
('528-160328', 0.029464720579791517),
('617-170505', 0.029423291891355983),
('600-170936', 0.02941077071629448),
('641-160328', 0.02941077071629448),
('642-160414', 0.02941077071629448),
('646-170505', 0.02941077071629448),
('655-170505', 0.02941077071629448),
('690-171032', 0.02941077071629448),
('772-171032', 0.02941077071629448),
('060-170065', 0.029381979540447915),
('216-140053', 0.029288345912008434),
('020-190221', 0.029283932072714066),
('040-180096', 0.029256218373636796),
('814-180011', 0.029250587380803456),
('Terminal Fazendinha', 0.02922981327700646),
('612-180090', 0.02921851139229471),
('050-180002', 0.029214746039337092),
('020-180110', 0.029208472607217154),
('303-108165', 0.029193427357017056),
('202-108023', 0.029182153587039447),
('631-150838', 0.029177145817059474),
('021-150208', 0.029175894143100654),
('021-180101', 0.029170888520995423),
('027-170016', 0.02916338330750832),
('020-150106', 0.029161507607527136),
('644-160076', 0.02915838197700906),
('021-140152', 0.029154007219767995),
('545-160080', 0.029141515143660462),
('814-190199', 0.029103480344170478),
('335-140500', 0.0290935204338865),
('513-150411', 0.029052507760641954),
('050-140288', 0.029038242620842314),
('515-140197', 0.029032044754663526),
('207-120060', 0.028995793170317596),
('213-130019', 0.028995793170317596),
('245-120019', 0.028995793170317596),
('545-160021', 0.02895725972038183),
('021-130208', 0.02888347229621166),
('649-150594', 0.02888163242834839),
('020-130128', 0.02884977858754339),
('637-160034', 0.028837545811683678),
('203-108034', 0.028825323405219455),
('214-130046', 0.028822269422276517),
('534-150120', 0.028815552937155656),
('020-140010', 0.028789327594249278),
('528-160330', 0.028484866829567256),
('617-170507', 0.028443171779630624),
('600-170938', 0.028442560490146335),
('641-160330', 0.028442560490146335),
('642-160416', 0.028442560490146335),
('646-170507', 0.028442560490146335),
('655-170507', 0.028442560490146335),
('690-171033', 0.028442560490146335),
('772-171033', 0.028442560490146335),
('060-170063', 0.028401598614497113),
('216-140350', 0.02830879645456712),
('020-190222', 0.028305261905015),
('814-180013', 0.028288975986873452),
('040-180142', 0.02827466607449011),
('040-180100', 0.02825352306348785),
('611-180001', 0.028248828910001775),
('612-180092', 0.028236514175153528),
('020-180112', 0.028225967230659798),
('303-108163', 0.0282136724159527),
('202-108021', 0.02820197302244398),
('631-150839', 0.02819554249088959),
('021-150200', 0.028193204842795166),
('021-170016', 0.028190867582290065),
('545-170121', 0.028185610162777836),
('027-170013', 0.02818327416127252),
('020-150107', 0.02817801957336542),
('644-160362', 0.028175684829842892),
('335-140502', 0.028124418179751382),
('814-190011', 0.0281226737413008),
('513-150269', 0.028082611298321403),
('050-140286', 0.028080872042063124),
('515-140195', 0.028061754432362924),
('207-120066', 0.02805308664813698),
('213-130483', 0.02805308664813698),
('245-120021', 0.02805308664813698),
('021-130869', 0.027925216301822983),
('649-150592', 0.027922350060465072),
('020-130375', 0.027893719974684105),
('637-160035', 0.027877712757121982),
('203-108036', 0.027868574021584488),
('214-130044', 0.027865719395355655),
('534-150029', 0.02785544758136216),
('528-160333', 0.02756808595146931),
('600-170940', 0.02753765279485643),
('641-160333', 0.02753765279485643),
('642-160419', 0.02753765279485643),
('646-170509', 0.02753765279485643),
('655-170509', 0.02753765279485643),
('690-171034', 0.02753765279485643),
('772-171034', 0.02753765279485643),
('617-170509', 0.027526244274926556),
('060-170061', 0.027484529416962934),
('216-140351', 0.02739264863955002),
('814-180015', 0.027390160883714033),
('020-190224', 0.0273898906756911),
('040-180129', 0.027340342120670855),
('611-180003', 0.027331552250396764),
('612-180388', 0.02731837803710501),
('020-180114', 0.027307409223775784),
('303-108161', 0.027297544820194978),
('545-160074', 0.027290424959782827),
('202-108019', 0.027285498000952754),
('631-150840', 0.02727783737783005),
('021-170013', 0.027274555570281238),
('021-150201', 0.027274555570281238),
('027-170011', 0.027266901089415572),
('020-150108', 0.027258704626162235),
('644-160244', 0.02725706592480403),
('335-140504', 0.027217796114967396),
('814-190012', 0.027205819566083877),
('050-140282', 0.027184614294617784),
('513-150267', 0.02717538131271843),
('207-120065', 0.027171297847553774),
('213-130041', 0.027171297847553774),
('Terminal Barreirinha', 0.027171297847553774),
('515-140328', 0.027154223445769697),
('021-130200', 0.027028501954207567),
('649-150590', 0.027024742923895246),
('020-130203', 0.02699899485600428),
('637-160037', 0.026979715979956673),
('203-108038', 0.026973295804820645),
('214-130042', 0.026970621633563254),
('534-150027', 0.02695725872697086),
('528-160335', 0.026708477867685664),
('600-170944', 0.026690036430020693),
('641-160335', 0.026690036430020693),
('642-160420', 0.026690036430020693),
('646-170511', 0.026690036430020693),
('655-170511', 0.026690036430020693),
('690-170561', 0.026690036430020693),
('772-170561', 0.026690036430020693),
('617-170511', 0.026666588786964703),
('060-170059', 0.0266248308965999),
('814-180017', 0.026548185818733385),
('216-140352', 0.026533939895158218),
('020-190226', 0.026531869640226573),
('040-180131', 0.026484342780145557),
('611-180005', 0.026471972458702208),
('612-180386', 0.02645806965270367),
('545-170491', 0.02645035217978601),
('020-180118', 0.026446752232957997),
('303-108159', 0.026439041359952873),
('202-109147', 0.026426713311291712),
('631-150841', 0.026417987897092446),
('021-170011', 0.026415935695748773),
('021-150203', 0.02641388381321842),
('027-170009', 0.026408242779534737),
('644-150272', 0.026396455673306726),
('335-140506', 0.026367800582435073),
('207-110131', 0.02634470726132321),
('213-130597', 0.02634470726132321),
('050-140278', 0.026343798749743297),
('513-150265', 0.026324934407692967),
('515-140193', 0.026303553543577808),
('021-130129', 0.026187585160961393),
('649-150588', 0.026183048331963343),
('020-130207', 0.026159884622768977),
('637-160244', 0.02613776634983658),
('203-108040', 0.02613374886346249),
('214-130040', 0.026131238561571776),
('534-150025', 0.02611518404234416),
('528-160336', 0.02590085613613938),
('600-170945', 0.025894437939781027),
('641-160336', 0.025894437939781027),
('642-160775', 0.025894437939781027),
('646-170910', 0.025894437939781027),
('655-170513', 0.025894437939781027),
('690-170563', 0.025894437939781027),
('772-170563', 0.025894437939781027),
('617-170513', 0.025859001936189344),
('060-170057', 0.02581728278566404),
('216-140048', 0.02572743258644781),
('020-190228', 0.025725972818744832),
('040-180133', 0.025680317194583337),
('611-180008', 0.025664811804854727),
('545-170492', 0.025660454287003767),
('612-180384', 0.025650292497416426),
('020-181052', 0.025638688874248312),
('303-108157', 0.025632890998690205),
('202-108015', 0.025620337926305692),
('631-150842', 0.02561069008012456),
('021-170009', 0.025609725695131053),
('021-150202', 0.025605868881336865),
('027-170007', 0.02560201322903679),
('335-140508', 0.025569287005761523),
('207-110008', 0.02556828965239069),
('213-130600', 0.02556828965239069),
('050-140283', 0.02555343529674048),
('513-150263', 0.025526101316371643),
('515-140190', 0.025504563129931292),
('021-130127', 0.025397415106251202),
('649-150586', 0.025392199836572128),
('020-130210', 0.025371360159022152),
('637-150751', 0.02534677550770527),
('203-108042', 0.02534488635398181),
('214-130022', 0.025342525307799),
('641-160061', 0.025146211804291524),
('642-160424', 0.025146211804291524),
('646-170544', 0.025146211804291524),
('655-170710', 0.025146211804291524),
('690-170739', 0.025146211804291524),
('772-170739', 0.025146211804291524),
('528-160338', 0.025140643221305183),
('617-170710', 0.02509889214388116),
('060-170050', 0.025057279508612036),
('216-140044', 0.02496850709190109),
('020-190230', 0.024967590463215103),
('040-180135', 0.024923671293550078),
('545-170145', 0.02491636644951541),
('611-180010', 0.02490541720855984),
('612-170373', 0.024890377705414576),
('020-180122', 0.0248785411867706),
('303-108155', 0.024874446552776833),
('202-108013', 0.024861716306510493),
('021-170007', 0.024851269062109396),
('631-150843', 0.024851269062109396),
('027-170006', 0.02484355282726335),
('207-110133', 0.024837611812890518),
('213-130601', 0.024837611812890518),
('335-140510', 0.02481771567737366),
('050-140605', 0.024809115232376305),
('513-150261', 0.024774321740592593),
('515-140189', 0.02475268162843019),
('021-130125', 0.02465353272153944),
('649-150583', 0.02464772516300322),
('020-130212', 0.024628980967000356),
('203-108044', 0.024602252945403986),
('637-150330', 0.024602252945403986),
('214-130020', 0.024600028228627415),
('641-160411', 0.024441249677357925),
('642-160733', 0.024441249677357925),
('646-170546', 0.024441249677357925),
('655-170515', 0.024441249677357925),
('690-170566', 0.024441249677357925),
('772-170566', 0.024441249677357925),
('528-160340', 0.024423783682494715),
('617-170515', 0.024382192282171394),
('060-170029', 0.0243407422935023),
('216-140043', 0.024253073262347474),
('020-120024', 0.024252640828126875),
('545-170141', 0.02421421584443863),
('040-180137', 0.024210336949708908),
('611-180021', 0.024189670481504784),
('612-170374', 0.024174193769802826),
('020-180125', 0.024162170012354486),
('303-108153', 0.024159595048853406),
('207-110187', 0.024148747873926922),
('213-130602', 0.024148747873926922),
('021-170006', 0.024136445050935953),
('631-150844', 0.024135588495581662),
('027-170003', 0.024128738240744605),
('335-140512', 0.024109065400760306),
('050-140284', 0.024106928981381958),
('513-150408', 0.02406555724147654),
('515-140007', 0.02404386199613759),
('021-130123', 0.023951986491142576),
('649-150582', 0.023945661588013093),
('020-130214', 0.02392881149893561),
('203-108046', 0.023901900626370556),
('637-150332', 0.023900220706450235),
('214-130018', 0.023899800763366816),
...]
# Calculando a centralidade de autovetor
eigenvector_centrality = nx.eigenvector_centrality(grafo)
# Colocando betweenness centrality em ordem decrescente
eigenvector_centrality = sorted(eigenvector_centrality.items(), key=lambda x: x[1], reverse=True)
# Exibindo a centralidade de autovetor
eigenvector_centrality
[('Terminal Capão Raso', 0.29881395094933444),
('Terminal Portão', 0.28470830394487123),
('Terminal Pinheirinho', 0.26031419340396744),
('Terminal Sítio Cercado', 0.14210691400289513),
('Terminal CIC', 0.1186468920998957),
('502-108056', 0.11848792800489215),
('507-109002', 0.11848792800489215),
('602-108057', 0.11848792800489215),
('020-170002', 0.11848792800489215),
('021-150169', 0.11848792800489215),
('023-109077', 0.11848792800489215),
('202-108056', 0.11848792800489215),
('607-109071', 0.11848792800489215),
('603-108056', 0.11848792800489215),
('X20-108056', 0.11848792800489215),
('Terminal Boqueirão', 0.11587703394250144),
('502-108122', 0.11288973228982815),
('602-108052', 0.11288973228982815),
('022-109066', 0.11288973228982815),
('202-108049', 0.11288973228982815),
('203-108052', 0.11288973228982815),
('216-150023', 0.11288973228982815),
('700-109002', 0.11288973228982815),
('024-109066', 0.11288973228982815),
('603-108049', 0.11288973228982815),
('050-170030', 0.11288973228982815),
('Terminal Campina do Siqueira', 0.1063363560466951),
('502-108064', 0.10321990682722944),
('508-109075', 0.10321990682722944),
('527-109075', 0.10321990682722944),
('528-150331', 0.10321990682722944),
('602-108123', 0.10321990682722944),
('040-170053', 0.10321990682722944),
('060-170983', 0.10321990682722944),
('350-108203', 0.10321990682722944),
('550-108203', 0.10321990682722944),
('600-150331', 0.10321990682722944),
('603-108064', 0.10321990682722944),
('610-109075', 0.10321990682722944),
('617-150331', 0.10321990682722944),
('631-150331', 0.10321990682722944),
('631-150845', 0.10321990682722944),
('641-150331', 0.10321990682722944),
('642-150331', 0.10321990682722944),
('646-150331', 0.10321990682722944),
('655-150331', 0.10321990682722944),
('690-150331', 0.10321990682722944),
('772-150331', 0.10321990682722944),
('X20-108064', 0.10321990682722944),
('Terminal Carmo', 0.09344638482051619),
('Terminal Hauer', 0.08698422384268119),
('502-108132', 0.05635604148871852),
('507-109076', 0.05635604148871852),
('508-109005', 0.05635604148871852),
('527-109005', 0.05635604148871852),
('534-150363', 0.05635604148871852),
('545-160023', 0.05635604148871852),
('546-109005', 0.05635604148871852),
('602-108098', 0.05635604148871852),
('637-160023', 0.05635604148871852),
('649-150610', 0.05635604148871852),
('X20-108132', 0.05635604148871852),
('040-180074', 0.04704622546248342),
('644-170086', 0.04704622546248342),
('612-170613', 0.04704622546248342),
('502-108053', 0.046983210194359463),
('507-109074', 0.046983210194359463),
('602-108059', 0.046983210194359463),
('020-170004', 0.046983210194359463),
('021-150070', 0.046983210194359463),
('202-108053', 0.046983210194359463),
('607-109035', 0.046983210194359463),
('603-108053', 0.046983210194359463),
('X20-108053', 0.046983210194359463),
('335-140480', 0.04598327139000443),
('502-108111', 0.04598327139000443),
('507-109006', 0.04598327139000443),
('513-150431', 0.04598327139000443),
('515-140296', 0.04598327139000443),
('545-150026', 0.04598327139000443),
('602-108095', 0.04598327139000443),
('X12-108111', 0.04598327139000443),
('502-108120', 0.044760911267023425),
('602-108054', 0.044760911267023425),
('202-108047', 0.044760911267023425),
('203-108054', 0.044760911267023425),
('216-150021', 0.044760911267023425),
('700-109074', 0.044760911267023425),
('603-108047', 0.044760911267023425),
('050-170015', 0.044760911267023425),
('020-190201', 0.04216112057572708),
('021-180127', 0.04216112057572708),
('022-109046', 0.04216112057572708),
('023-109067', 0.04216112057572708),
('024-109067', 0.04216112057572708),
('024-109047', 0.04216112057572708),
('027-180127', 0.04216112057572708),
('303-108187', 0.04216112057572708),
('304-109044', 0.04216112057572708),
('814-190001', 0.04216112057572708),
('502-108062', 0.040928200311953246),
('528-170051', 0.040928200311953246),
('602-108125', 0.040928200311953246),
('040-170054', 0.040928200311953246),
('060-170123', 0.040928200311953246),
('350-108205', 0.040928200311953246),
('550-108205', 0.040928200311953246),
('600-160301', 0.040928200311953246),
('603-108062', 0.040928200311953246),
('617-160301', 0.040928200311953246),
('631-170051', 0.040928200311953246),
('631-150846', 0.040928200311953246),
('641-170051', 0.040928200311953246),
('642-170051', 0.040928200311953246),
('646-160301', 0.040928200311953246),
('655-160301', 0.040928200311953246),
('690-160301', 0.040928200311953246),
('772-160301', 0.040928200311953246),
('X20-108062', 0.040928200311953246),
('502-108094', 0.037092339116411355),
('503-108094', 0.037092339116411355),
('508-109040', 0.037092339116411355),
('602-108091', 0.037092339116411355),
('502-108088', 0.03451401628641807),
('503-108088', 0.03451401628641807),
('505-109040', 0.03451401628641807),
('602-108085', 0.03451401628641807),
('020-150204', 0.03451401628641807),
('021-140013', 0.03451401628641807),
('022-109077', 0.03451401628641807),
('023-109065', 0.03451401628641807),
('502-108130', 0.022350006212938502),
('534-150364', 0.022350006212938502),
('545-160025', 0.022350006212938502),
('602-108100', 0.022350006212938502),
('637-160025', 0.022350006212938502),
('649-150609', 0.022350006212938502),
('X20-108130', 0.022350006212938502),
('040-180076', 0.018654622812277817),
('644-170084', 0.018654622812277817),
('612-170611', 0.018654622812277817),
('502-108051', 0.018629641061068253),
('507-110457', 0.018629641061068253),
('602-108061', 0.018629641061068253),
('020-170005', 0.018629641061068253),
('021-150071', 0.018629641061068253),
('202-108051', 0.018629641061068253),
('607-109068', 0.018629641061068253),
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('040-180172', 2.250058338645856e-08),
('611-180027', 2.250058338645856e-08),
('545-170145', 2.228647426871066e-08),
('637-150330', 2.228647426871066e-08),
('649-150583', 2.228647426871066e-08),
('050-140605', 2.171768811337057e-08),
('040-180174', 2.151398068995699e-08),
('611-180029', 2.151398068995699e-08),
('020-190230', 2.0957479181339647e-08),
('021-170007', 2.0957479181339647e-08),
('027-170006', 2.0957479181339647e-08),
('303-108155', 2.0957479181339647e-08),
('020-130214', 2.010048448144565e-08),
('203-108046', 2.010048448144565e-08),
('207-110187', 2.010048448144565e-08),
('213-130602', 2.010048448144565e-08),
('040-180176', 1.9994919057136643e-08),
('611-180031', 1.9994919057136643e-08),
('528-160338', 1.8440020934218457e-08),
('060-170050', 1.8440020934218457e-08),
('617-170710', 1.8440020934218457e-08),
('631-150843', 1.8440020934218457e-08),
('641-160061', 1.8440020934218457e-08),
('642-160424', 1.8440020934218457e-08),
('646-170544', 1.8440020934218457e-08),
('655-170710', 1.8440020934218457e-08),
('690-170739', 1.8440020934218457e-08),
('772-170739', 1.8440020934218457e-08),
('612-170373', 1.814496530595391e-08),
('040-180178', 1.7970024463285328e-08),
('611-180033', 1.7970024463285328e-08),
('202-108013', 1.768438586831676e-08),
('216-140044', 1.768438586831676e-08),
('020-180122', 1.7667794851067154e-08),
('021-130125', 1.732605259157353e-08),
('214-130016', 1.5932266435144048e-08),
('040-190079', 1.5702427609195814e-08),
('303-108189', 1.568806129573777e-08),
('040-190077', 1.568806129573777e-08),
('Terminal Campo Comprido', 1.5679952154612977e-08),
('303-108191', 1.566220204799298e-08),
('040-190075', 1.566220204799298e-08),
('040-190081', 1.564783561805525e-08),
('303-108201', 1.564549029954727e-08),
('X02-108189', 1.564549029954727e-08),
...]
# Exibindo o coeficiente de clusterização
print(nx.average_clustering(nx.Graph(grafo)))
3.85628524024115e-06
dicDegree = dict(grafo.degree() )
valores = sorted(set(dicDegree.values()))
valores
hist = [list(dicDegree.values()).count(x) for x in valores]
plt.plot(valores, hist, 'ro-')
plt.xlabel('Grau')
plt.ylabel('Numero de nós')
Text(0, 0.5, 'Numero de nós')
É interessante notar que boa parte dos nós tem baixo grau. Baseando-se no ranqueamento disponível na Seção 4.3 é possível afirmar que os nós de maior graus são terminais, podendo portando serem tratados como hubs.
nx.draw(grafo, with_labels=False)
# No layout circular, todos os nós são colocados na circunferência de um círculo.
# As conexões de cada nó para outros nós conectados são indicadas pelas linhas que conectam esses pontos.
# Isso ajuda a mostrar a distribuição de densidade das conexões e a distância entre os nós de conexão.
plt.figure(figsize=(10,10))
pos = nx.circular_layout(grafo)
nx.draw_networkx(grafo, pos, with_labels=False, edge_color='.4')
plt.axis('off')
plt.tight_layout();
# Neste layout os nós são colocados aleatoriamente dentro de uma área.
# As conexões entre os nós são desenhadas com linhas. O layout ajuda a entender a distribuição aleatória da rede.
plt.figure(figsize=(50,50))
pos = nx.random_layout(grafo)
nx.draw_networkx(grafo, pos, with_labels=False)
plt.axis('off')
plt.tight_layout();